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Popular >

integral of-(x+1)

Solution

\int - (x + 1) d x

Solution

- \frac{x ^{2}}{2} - x + C

Solution steps

\int - (x + 1) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int x + 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - (\int x d x + \int 1 d x)

\int x d x = \frac{x ^{2}}{2}

\int 1 d x = x

= - (\frac{x ^{2}}{2} + x)

Simplify

= - \frac{x ^{2}}{2} - x

Add a constant to the solution

= - \frac{x ^{2}}{2} - x + C

Popular Examples

integral of 8^{2x}

\int 8^{2 x} d x

integral of 3t^2-10t+19

\int 3 t^{2} - 10 t + 19 d t

integral of \sqrt[5]{5x+7}

integral of (3x^2+1)/(x^3+x^2+x+1)

\int \frac{3 x ^{2} + 1}{x ^{3} + x ^{2} + x + 1} d x

integral of 3^{2x}(2^{1-x}+1)

\int 3^{2 x} (2^{1 - x} + 1) d x

Frequently Asked Questions (FAQ)

What is the integral of-(x+1) ?
The integral of-(x+1) is -(x^2)/2-x+C